ADER (Arbitrary high order by DERivatives) and Lax-Wendroff (LW) schemes are two high order single stage methods for solving time dependent partial differential equations. ADER is based on solving a locally implicit equation to obtain a space-time predictor solution while LW is based on an explicit Taylor's expansion in time. We cast the corrector step of ADER Discontinuous Galerkin (DG) scheme into an equivalent quadrature free Flux Reconstruction (FR) framework and then show that the obtained ADER-FR scheme is equivalent to the LWFR scheme with D2 dissipation numerical flux for linear problems. This also implies that the two schemes have the same Fourier stability limit for time step size. The equivalence is verified by numerical experiments.

翻译：ADER（任意高阶导数方法）和Lax-Wendroff（LW）格式是求解含时偏微分方程的两种高阶单步方法。ADER基于求解局部隐式方程以获得时空预测解，而LW则基于显式泰勒时间展开。我们将ADER间断伽辽金（DG）格式的校正步骤转化为等效的无求积通量重构（FR）框架，进而证明所得ADER-FR格式与采用D2耗散数值通量的LWFR格式在线性问题中等价。这一结论也表明两种格式在时间步长上具有相同的傅里叶稳定性极限。数值实验验证了该等价性。